Skip to main content
Log in

New clustering methods for interval data

  • Published:
Computational Statistics Aims and scope Submit manuscript

Summary

In this paper we propose two clustering methods for interval data based on the dynamic cluster algorithm. These methods use different homogeneity criteria as well as different kinds of cluster representations (prototypes). Some tools to interpret the final partitions are also introduced. An application of one of the methods concludes the paper.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Figure 1:
Figure 2:

Similar content being viewed by others

References

  • Bock, H.-H. (2001), Clustering algorithms and kohonen maps for symbolic data, in ‘ICNCB Proceedings’, Osaka, pp. 203–215.

  • Bock, H.-H. & Diday, E., eds (2000), Analysis of symbolic data. Exploratory methods for extracting statistical information from complex data, Studies in classification, data analysis and knowledge organisation, Springer Verlag, Heidelberg.

    MATH  Google Scholar 

  • Celeux, G., Diday, E., Govaert, G., Lechevallier, Y. & Ralambondrainy, H. (1989), Classification automatique des donnes, Dunod.

  • Chavent, M. (2004), An hausdorff distance between hyper-rectangles for clustering interval data, in D. Banks, L. House, F. McMorris, P. Arabie & W. Gaul, eds, ‘Classification, Clustering, and Data Mining applications’, Springer Verlag, pp. 333–339.

  • Chavent, M., De Carvalho, F. A. T., Lechevallier, Y. & Verde, R. (2003), ‘Trois nouvelles méthodes de classification automatique de données symboliques de type intervalle’, Rev. Stat. Appliquées LI(4), 5–29.

    Google Scholar 

  • Chavent, M. & Lechevallier, Y. (2002), Dynamical clustering of interval data. optimization of an adequacy criterion based on hausdorff distance, in K. Jajuga, A. Sokolowski & H.-H. Bock, eds, ‘Classification, Clustering, and Data Analysis’, Springer Verlag, Berlin, pp. 53–60.

    Chapter  Google Scholar 

  • De Carvalho, F. A. T. (1995), ‘Histograms in symbolic data analysis.’, Annals of Operations Research 55, 289–322.

    Article  Google Scholar 

  • De Carvalho, F. A. T. & Souza, R. M. C. (1998), Statistical proximity functions of boolean symbolic objects based on histograms, in A. Rizzi, M. Vichi & H.-H. Bock, eds, ‘Advances in Data Science and Classification’, Springer Verlag, pp. 391–396.

  • De Carvalho, F. A. T., Verde, R. & Lechevallier, Y. (1999), A dynamical clustering of symbolic objects based on a context dependent proximity measure., in H. e. a. Barcelar, ed., ‘Proceedings of the IX International Symposium on Applied Stochastic Models and Data analysis’, Universidade de Lisboa, pp. 237–242.

  • De Souza, R. M. C. R. & De Carvalho, F. A. T. (2004), ‘Clustering of interval data based on city-block distances.’, Pattern Recognition Letters 25(3), 353–365.

    Article  Google Scholar 

  • Diday, E. (1971), ‘La méthode des nuées dynamiques’, Rev. Stat. Appliquées 19(2).

  • Diday, E. (1988), The symbolic approach in clustering and related methods of data analysis: The basic choices, in H.-H. Bock, ed., ‘Classification and related methods of data analysis’, North Holland, Amsterdam, pp. 673–684.

    Google Scholar 

  • Diday, E. & Brito, P. (1989), Symbolic cluster analysis, in O. Opitz & H.-H. Bock, eds, ‘Conceptual and Numerical Analysis of Data’, Springer Verlag, Berlin, pp. 45–84.

    Chapter  Google Scholar 

  • Diday, E. & Simon, J. C. (1976), Clustering analysis, in K. Fu, ed., ‘Digital Pattern Classification’, Springer Verlag, pp. 47–94.

  • Gordon, A. D. (2000), An interactive relocation algorithm for classifying symbolic data., in W. e. a. Gaul, ed., ‘Data Analysis: Scientific Modeling and Practical Application’, Springer Verlag, Berlin, pp. 17–23.

    Chapter  Google Scholar 

  • Huttenlocher, D. P., Klanderman, G. A. & Rucklidge, W. J. (1993), ‘Comparing images using the hausdorff distance’, IEE Transaction on Pattern Analysis and Machine Intelligence 15, 850–863.

    Article  Google Scholar 

  • Nadler, S. B. J. (1978), Hyperspaces of sets, Marcel Dekker, Inc., New York.

    MATH  Google Scholar 

  • Ralambondrainy, H. (1995), ‘A conceptual version of the k-means algorithm.’, Pattern Recognition Letters 16, 1147–1157.

    Article  Google Scholar 

  • Rote, G. (1991), ‘Computing the minimum hausdorff distance between two point sets on a line under translation’, Information Processing Letters 38, 123–127.

    Article  MathSciNet  Google Scholar 

  • Verde, R., De Carvalho, F. A. T. & Lechevallier, Y. (2000), A dynamical clustering algorithm for multi-nominal data, in H. A. L. K. et al., ed., ‘Data Analysis, Classification and Related methods’, Springer Verlag, pp. 387–394.

Download references

Acknowledgements

The second author would like to thank CNPq and FACEPE (Brazilian Agencies) for their financial support.

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Chavent, M., de Carvalho, F.d.A.T., Lechevallier, Y. et al. New clustering methods for interval data. Computational Statistics 21, 211–229 (2006). https://doi.org/10.1007/s00180-006-0260-0

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00180-006-0260-0

Keywords

Navigation